Chapter 7.4, Problem 3Q

To determine

The polynomial in standard form and identify the degree and leading coefficient of the polynomial and also classify the polynomial by the number of terms.

Explanation of Solution

Given information:

The give polynomial is $\frac{2}{3}{m}^4-\frac{5}{6}{m}^6$ .

Calculations:

Here the given polynomial is $\frac{2}{3}{m}^4-\frac{5}{6}{m}^6$ .

So we can see that the polynomial has two terms. So it is called a binomial.

Here the term, $\frac{2}{3}{m}^4$ has a degree of $4$ .

Also the term, $-\frac{5}{6}{m}^6$ has a degree of $6$ .

Now arranging the terms according to descending order of degree we get the standard form of the polynomial. Thus the standard form of the polynomial is as follows.

  $-\frac{5}{6}{m}^6+\frac{2}{3}{m}^4$

Here the highest degree of the two terms is $6$ . So the degree of the polynomial is $6$ .

The coefficient of the term having degree $6$ is $-\frac{5}{6}$ . So the leading coefficient of the polynomial is $-\frac{5}{6}$

Thus the expression is called a sixth degree polynomial.